1. Field of the Invention
This invention involves the correction of position information obtained from the global positioning system (GPS), and more specifically to the correction of GPS position information for errors induced by the GPS satellites orbit about the earth and the sun.
2. Description of the Related Art
The complete global positioning system (GPS) constellation involves twenty-four satellites separated by large distances, each possessing a highly accurate clock and a microwave source with precise frequency. The problem of transforming the frequency of coherent radio signals to the geocentric inertial coordinate frame (as required during the transfer of time information) involves an implicit, dependence on earth-sun-clock orientation that has been omitted, except in very-long-baseline interferometry (VLBI). To obtain the required time standard between satellites in the GPS system, each satellite in the system has an atomic (Cs or Rb) clock possessing a frequency that is accurate to one part in .about.10.sup.13 -10.sup.14. See, Copps, An Aspect of the Role of the Clock in a GPS Receiver, Navigation, Vol. 31, No. 3, pp. 233-242, 1984; Knable et al., Clock Coasting and Altimeter Error Analysis for GPS, Navigation, Vol. 31, No. 4, pp.289-302, 1984, which are hereby incorporated in their entirety by reference for all purposes. The orbit of each satellite is approximately circular (possessing an eccentricity of .about.10.sup.-3), has a 12 hour period and is located in one of three orbital planes. Each orbital plane intersects the plane of the equator at an angle of 55O. The signal from each GPS satellite includes a frequency offset .LAMBDA. (.about.1 part on 10.sup.10). This offset automatically accounts for important earth-induced gravitational blue-shift and second order Doppler effects (SDE's), which insure that GPS clocks are synchronized, based on the same procedure used in defining universal time (UT), and that GPS transmissions effectively are altered in a manner that would make them appear to originate from a frame that is stationary in the frame of the moving geoid defined by the surface of the ocean at the surface of the earth. As a consequence, time is being maintained and defined in effectively the same manner both in GPS satellites and through UT (as defined at the surface of the ocean).
The GPS is used to determine position by correlating information from coherent microwave transmissions provided by the constellation of satellites. See; Milliken et al., Principle of Operation of NAVSTAR and System Characteristics, Navigation, Vol. 25, No, 2, pp. 95-106, 1978 and Spilker, GPS Signal Structure and Performance Characteristics, Navigation, Vol. 25, No, 2, pp. 121-146, 1978, which are hereby incorporated in their entirety by reference for all purposes. The accuracy of this procedure is determined by non-systematic and systematic errors. Systematic errors are associated with known, appreciable effects that result from the inaccuracies of the frequency and of the length of the path of each signal from the satellite to a potential user. Non-systematic errors are inaccuracies in the determination of path length and frequency that can not be eliminated because they are the result of the known limitations of the existing procedures for determining these quantities. Optimal performance requires that non-systematic errors be minimized and systematic errors be eliminated.
An anomalous absolute error of 1-10 feet in user position relative to each GPS satellite exists as a consequence of an error in the determination of path length and/or frequency, and this absolute error varies periodically in the transmission from each GPS satellite as a function of time in a regular fashion: maximal and minimal errors from this effect occur approximately once every 12 hours. This anomalous error has been previously thought to be the result of an unknown ionospheric effect that has not been systematically removed by existing procedures. M. Weiss reported in Weiss, Apparent Diurnal Effects in the Global Positioning System, IEEE Trans. Instr. and Meas., Vol. 38, NO. 5, pp. 991-997, Oct. 1989, which is hereby incorporated in its entirety by reference for all purposes, a large, systematic variation in the Allan variance (See; Blair, Time and Frequency: Theory and Fundamentals, Nat. Bur. of Stds., Vol. 140, pp. 151-205, 1974, which is hereby incorporated by reference in its entirety for all purposes) between GPS time and UT (corresponding to a systematic variation of the normalized variance of the difference between measured clock frequencies provided by GPS and UT). These variations 1) occur in the transmissions provided by all satellites, 2) have their maximal peak-to-peak variation diurnally, and have maximal magnitude (when averaged over one-half day) corresponding to a deviation between GPS time and UT of 1-10 nanoseconds.
It has been assumed that orbital motion of the earth around the sun does not alter the frequency of the signal from a GPS satellite between the points of transmission and reception. As a consequence, no attempt has been made to incorporate known sun-induced variations in the frequencies of radio transmissions that have been identified from VLBI, as stated above. Because this effect is neglected in all GPS signals, the frequencies from all GPS transmissions as they are received will be different from the value that they are supposed to have by an amount that may be accounted for by a systematic correction that applies only during the time interval .DELTA.t required for the signal to reach the earth. A comparable trend in the Allan variance involving a regular, periodic variation, with period of one day (and maximal peak-to-peak variation occurring diurnally) can be inferred from the product of the maximum values of the time interval .DELTA.t.sub.max (.about.0.1 s) required for the signal to reach the earth and the fractional deviation in frequency .DELTA.f/f.sub.o .vertline..sub.max that results from the sun-induced effects outlined herein. This means the effect is not accumulative as it would be if it affected the accuracy of time-keeping and can be derived from the product of .DELTA.t with the deviation in frequency from the correct value. The resulting correction is periodic (with a period of one day) and has a maximal fractional magnitude of .about.10.sup.-8. Because the value of .DELTA.t is roughly 0.1 seconds, the resulting correction, on the average, for the difference between time "reported" by the GPS at the earth surface and UT is 1-10 nanoseconds during a twelve hour period. These deviations between UT and GPS time should be systematic, meaning that they should be seen in the reported time that is sent by all satellites.
The anomalous 1-10 foot error in the GPS has been determined not to be the result of ionospheric effect but occurs because of variations in the frequency of each of the two GPS L-band transmissions (for developing the C/A and P-codes) that are the result of known special and general relativistic effects (previously identified in very-long baseline interferometry (VLBI)) that result because each satellite orbits around both the sun and the earth. See; Chubb, Sun-Induced Variations in Time in the Global Positioning System, Astrophy. and Space Sc., Vol. 213, pp. 63-74, 1994, which is hereby incorporated in its entirety by reference for all purposes; Wiess, supra; Milliken et al., supra; and Spilker, supra. It is known from VLBI that because each satellite orbits in this fashion, in order to systematically account for changes in frequency occurring between points of reception and transmission, it is necessary to include the gravitationally and orbitally induced red- and blue-shifts in the frequency of GPS transmissions that result from the relative orientation and motion of each GPS satellite about the sun.